Banach-Tarski paradox

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Banach-Tarski paradox [¦bä‚näk ¦tär·skē ′par·ə‚däks]

(mathematics)

A theorem stating that, for any two bounded sets, with interior points in a Euclidean space of dimension at least three, one of the sets can be disassembled into a finite number of pieces and reassembled to form the other set by moving the pieces with rigid motions (translations and rotations).

(mathematics)

Banach-Tarski paradox - It is possible to cut a solid ball into finitely many pieces (actually about half a dozen), and then put the pieces together again to get two solid balls, each the same size as the original.

This paradox is a consequence of the Axiom of Choice.

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No references found			The Banach-Tarski paradox, string theory, Klein bottles, and universes where time runs in reverse are some subjects explored. The Jinn from hyperspace, and other scribblings--both serious and ... by SciTech Book News Far more mind-blowing is a mathematical result known as the Banach-Tarski paradox after two Polish mathematicians, Stefan Banach and Alfred Tarski. Hotel Infinity by Gardner, Martin / New Criterion However, even by the time he came to the US, Tarski was already established as a master in such matters as the Banach-Tarski Paradox (in which a sphere of any size can be cut up into a finite number of pieces and re-assembled into a sphere of any other size) and his advances in logic and set theory. Alfred Tarski; life and logic by SciTech Book News			Bamboo Bambundu Bamburgh Bambusoideae Bambuti Bamenda bamf Bamford, Samuel Bamian Bamileke bamli Bampton, John Bampton, Rose Ban Ban Ki-moon Ban, Frigyes Bán, Frigyes Bana Banaba Banach algebra Banach inverse mapping theorem Banach Space Banach's fixed-point theorem Banach, Stefan Banach-Steinhaus theorem Banach-Tarski paradox banakite Banality Banana banana connector banana fish banana freckle banana jack banana label banana oil banana plug banana problem banana republic Bananal Island Banat Banbridge Banbury Banca Nationala a Romaniei Banca Nationala a României Banca Nazionale del Lavoro Bancila, Octav banco Bancroft Bancroft Agreements Bancroft's Filaria Bancroft's filariasis			BANAA Banaadir Banaan Banaan Banaan Banaba Banaba Banaba Island Banaba Island Banaban BANAC Banach Banach -algebra Banach algebra Banach algebras Banach Center Publications Banach completion Banach function space Banach inverse mapping theorem Banach norm Banach ring Banach space Banach spaces Banach's fixed point theorem Banach's fixed-point theorem Banach, Stefan Banach-Schauder theorem Banach-Steinhaus theorem Banach-Tarski paradox* Banados-Teitelboim-Zanelli BANAGAS Banaias banak banakite banal banal banal banalities banalities banalities banality banality banality banalize banalize banally banally Banamex Banamex Banamine banana banana banana banana banana Banana (disambiguation) Banana (fruit) Banana (fruit) Banana (fruit)

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